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What is the sum of the series:- 1/10 + 2/10^2 + 3/10^3.......to infinity ?

What is the sum of the series:-
1/10 + 2/10^2 + 3/10^3.......to infinity ?

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
Given series1/10 + 2/10^2 + 3/10^3.......to infinity
x + 2x^2 + 3x^3 + 4x^4 + ...
where x=1/10=0.1
this series is AGP where r=1/10 and a=1,d=1
=(a/1-r)+(dr/(1-r)2)
where a=1,d=1,r=0.1
=1.23456

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